Upside capture, downside capture and the ratio between them worked on twelve months of one fund, with the Excel formula and the sorting error that flatters a manager.
Upside capture is the fund's compound return in the months the benchmark rose, divided by the benchmark's compound return in the same months; downside capture is the same ratio over the months it fell. On an illustrative twelve-month record the fund captures 83.7 per cent of the upside and 72.0 per cent of the downside, a capture ratio of 1.16. The months are sorted by the benchmark, never by the fund.
Worked in full in Asset Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An equity fund and its benchmark over twelve months. The returns are illustrative. Seven months were up for the benchmark and five were down.
| Month | Benchmark | Fund | Benchmark month |
|---|---|---|---|
| 1 | 2.1 | 1.8 | up |
| 2 | −1.4 | −0.9 | down |
| 3 | 3.0 | 2.5 | up |
| 4 | −2.6 | −1.7 | down |
| 5 | 1.2 | 1.1 | up |
| 6 | 0.8 | 0.9 | up |
| 7 | −3.5 | −2.6 | down |
| 8 | 2.4 | 1.9 | up |
| 9 | −0.9 | −0.4 | down |
| 10 | 1.7 | 1.5 | up |
| 11 | −1.8 | −1.5 | down |
| 12 | 2.9 | 2.3 | up |
| Twelve months, compounded | 3.68 | 4.84 |
The fund lagged the benchmark in six of the seven rising months and still finished the year 1.16 points ahead, because it lost much less in the falling ones. Capture ratios put a number on that pattern.
Up-market months are those in which the benchmark's return was positive: 1, 3, 5, 6, 8, 10 and 12. Down-market months are the other five. The fund's own sign plays no part. Month 6, where the fund beat a rising market, is an up month; a month where the fund fell while the benchmark rose would still be an up month, and would count against the fund.
Up-market return = (Π(1 + r) over the up months)12/n − 1, with n = 7
Benchmark: 1.149612/7 − 1 = 26.99%. Fund: 1.126212/7 − 1 = 22.61%
Upside capture = 22.61 / 26.99 = 83.7
Down months, n = 5. Benchmark: 0.901912/5 − 1 = −21.95%. Fund: 0.930912/5 − 1 = −15.80%
Downside capture = −15.80 / −21.95 = 72.0
Excel, fund returns in B2:B13 and benchmark in C2:C13 as decimals, entered as one formula:=(PRODUCT(IF(C2:C13>0,1+B2:B13,1))^(12/COUNTIF(C2:C13,">0"))-1)/(PRODUCT(IF(C2:C13>0,1+C2:C13,1))^(12/COUNTIF(C2:C13,">0"))-1)
The cumulative returns behind the powers are 14.96 per cent for the benchmark and 12.62 per cent for the fund over the up months, and −9.81 and −6.91 per cent over the down months. Annualising is a common geometric convention among fund data providers; others take the geometric mean monthly return of each subset without annualising, which on this record gives 85.2 and 69.6. Either way, a capture ratio on a factsheet will not match a simple average of monthly ratios.
The fund keeps 83.7 per cent of the market's gains and suffers 72.0 per cent of its losses. Below 100 on the downside is protection; below 100 on the upside is the price paid for it. The ratio of the two, 83.7 / 72.0 = 1.16, is the number to compare across managers: above 1.00 the fund converts market movement into relative return in its favour, and the twelve months confirm it with 4.84 per cent against 3.68.
The arithmetic method, averaging the up-month returns and dividing, gives 85.1 and 69.6 on the same data, a ratio of 1.22. Neither is wrong, but they are not comparable. State the method beside the figure, and never set one manager's arithmetic capture beside another's geometric capture.
Capture ratios describe a shape, not a return. The table runs fictional funds through one rising month and one falling month of the same size, a market that goes nowhere and loses a little to compounding.
| Upside capture | Downside capture | Capture ratio | Fund, ±3.0% months | Fund, ±6.0% months |
|---|---|---|---|---|
| 100 | 100 | 1.00 | −0.09% | −0.36% |
| 110 | 115 | 0.96 | −0.26% | −0.76% |
| 120 | 100 | 1.20 | 0.49% | 0.77% |
| 82 | 69 | 1.19 | 0.34% | 0.58% |
| 90 | 70 | 1.29 | 0.54% | 0.97% |
| 70 | 50 | 1.40 | 0.57% | 1.07% |
The benchmark row is the first: −0.09 and −0.36 per cent. A fund with 110 up and 115 down looks aggressive and exciting in a rally and loses more than twice what the benchmark loses over the round trip. A defensive 70 and 50 fund wins in a choppy market but would trail badly in a year of seven straight rising months. That is why a capture ratio needs at least a full market cycle of data, and why twelve months, as here, is a description and not a verdict.
A downside capture below 100 is closely related to the Sortino ratio, which penalises only the bad months: see how to calculate the Sortino ratio. For the beta behind an asymmetric capture pair, Jensen's alpha and beta work on the same kind of record.
The mandate's own returns, risk ratios and the record of every three-year window are in the free workbooks for this book.
What matters is the pair: upside capture above downside capture, so their ratio is above 1.00. A fund at 83.7 upside and 72.0 downside has a ratio of 1.16 and, in the worked year, returned 4.84 per cent against the benchmark's 3.68. A fund at 110 up and 115 down has a ratio of 0.96 and loses more than the benchmark over a round trip, however strong it looks in a rally.
Fund data providers generally compound the returns of the selected months, and many annualise the result, which is the geometric method used here. The arithmetic method averages monthly returns instead. On the same twelve months the geometric method gives 83.7 and 72.0 and the arithmetic 85.1 and 69.6, so two factsheets can disagree without either being wrong. Compare managers on one method only.
Enough to include a full market cycle, typically three to five years of monthly returns. With twelve months, as in the worked case, there are only seven up months and five down months, and a single month such as the 3.5 per cent fall in month 7 moves the downside figure materially. Treat a one-year capture ratio as a description, not evidence of skill.
This article is one calculation from Asset Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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